function that detects if a ray is intersecting an object - actionscript-3

Question

I have a function that detects if a ray is intersecting an object, but it works with a radius around the center of the object, I want it to work with a bounding box, I want to give it 2 Vector3D of the bounding box, and one vector of the origin of the ray and one of the direction of the ray, and it will calculate if there is an intersection, can anyone help me with that? what is the mathematical formula for this?
intersectRay(origin:Vector3D, dir:Vector3D):

Answer 1

Found the solution.
1. I use a bounding box of 8 points, each for each corner.
2. I used this function to give each point a location of x and y on a 2D plain this way I turned the 3D problem into a 2D problem, the x and y are really the horizontal angle of the point relative to the camera position and the vertical angle relative to the camera position point:
public function AngleBetween2vectors(v1:Vector3D,v2:Vector3D):Point
{
var angleX:Number = Math.atan2(v1.x-v2.x,v1.z-v2.z);
angleX = angleX*180/Math.PI;
var angleY:Number = Math.atan2(v1.y-v2.y,v1.z-v2.z);
angleY = angleY*180/Math.PI;
return new Point(angleX,angleY);
}
Then I use a convex hull algorithm to delete the point that are not part of the external outline polygon which marks the place of the object on the screen, can be found on the net, make sure the bounding box doesn't contain duplicate points like if you have a flat plain with no depth, this can cause problem for the algorithm, so when you create the bounding box clean them out.
Then I use this algorithm to determine if the point of the mouse click falls within this polygon or outside of it:
private function pnpoly( A:Array,p:Point ):Boolean
{
var i:int;
var j:int;
var c:Boolean = false;
for( i = 0, j = A.length-1; i < A.length; j = i++ ) {
if( ( ( A[i].y > p.y ) != ( A[j].y > p.y ) ) &&
( p.x < ( A[j].x - A[i].x ) * ( p.y - A[i].y ) / ( A[j].y - A[i].y ) + A[i].x ) )
{
c = !c;
}
}
return c;
}
Then I measure the distance to the object and pick the closest one to the camera position, using this function:
public function DistanceBetween2Vectors(v1:Vector3D,v2:Vector3D):Number
{
var a:Number = Math.sqrt(Math.pow((v1.x-v2.x),2)+Math.pow((v1.y-v2.y),2));
var b:Number = Math.sqrt(Math.pow((v1.z-v2.z),2)+Math.pow((v1.y-v2.y),2));
return Math.sqrt(Math.pow(a,2)+Math.pow(b,2));
}
I'm sure there are more efficient ways, but this way is an interesting one, and it's good enough for me, I like it because it is intuitive, I don't like to work with abstract mathematics, it's very hard for me, and if there is a mistake, it's very hard to find it. If anyone has any suggestions on how I can make it more efficient, I'll be happy to hear them.